Optimal Scaling of Mala for Nonlinear Regression

Breyer, Laird Arnault; Piccioni, Mauro; Scarlatti, Sergio

Optimal Scaling of Mala for Nonlinear Regression

Authors

Breyer, Laird Arnault

Piccioni, Mauro

Scarlatti, Sergio

Description

We address the problem of simulating efficiently from the posterior distribution over the parameters of a particular class of nonlinear regression models using a Langevin-Metropolis sampler. It is shown that as the number N of parameters increases, the proposal variance must scale as N{-1/3} in order to converge to a diffusion. This generalizes previous results of Roberts and Rosenthal [J. R. Stat. Soc. Ser. B Stat. Methodol. 60 (1998) 255-268] for the i.i.d. case, showing the robustness of their analysis.